PPT-Inducing,Distillation-Prohibiting,and Entanglement-Binding Quantum Channels

We review the entanglement degradation in open quantum systems in the Choi–Jamio?kowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. We clarify the relation between the above channels and entanglement-binding channels. We give an example of the distillation-prohibiting map Φ ? Φ, where Φ is not entanglement binding.     

Probing structural integrity of single walled carbon nanotubes by dynamic and static compression

We report on a first study of single walled carbon nanotubes (SWCNTs) after application of dynamic (shock) compression. The experiments were conducted at 19 GPa and 36 GPa in a recovery assembly. For comparison, an experiment at a static pressure of 36 GPa was performed on the material from the same batch in a diamond anvil cell (DAC). After the high pressure treatment the samples were characterized by Raman spectroscopy and transmission electron microscopy (TEM). After exposure to 19 GPa of shock compression the CNT material exhibited substantial structural damage such as CNT wall disruption, opening of the tube along its axis (“unzipping”) and tube shortening (“cutting”). Dynamic compression to 36 GPa resulted in essentially complete CNT destruction whereas at least a fraction of the nanotubes was recovered after 36 GPa of static compression though severely damaged. The results of these shock wave experiments underline the prospect of using SWCNTs as reinforcing units in material WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Contribution to the General Linear Conjugation Problem for A Piecewise Analytic Vector

Establishing an analogy between the theories of Riemann–Hilbert vector problem and linear ODEs, for the n-dimensional homogeneous linear conjugation problem on a simple smooth closed contour Γ partitioning the complex plane into two domains D⁺ and D^? we show that if we know n?1 particular solutions such that the determinant of the size n?1 matrix of their components omitting those with index k is nonvanishing on D⁺ ∪ Γ and the determinant of the matrix of their components omitting those with index j is nonvanishing on Γ ∪ D^? {∞}, where \(k,j = \overline {1,n} \), then the canonical system of solutions to the linear conjugation problem can be constructed in closed form.     

Elastic moduli of η‐Ta2N3, a tough self‐healing material,via laser ultrasonics

The elastic moduli of the dense polycrystalline oxygen‐bearing η‐Ta₂N₃, a novel hard and tough high‐pressure (HP) material, were measured using the laser ultrasonic technique. The bulk modulus was determined to be B₀ = 281(15) GPa which is only ～11% below that from HP compression measurements. Our value of the shear modulus G₀ = 123(2) GPa is below those ones predicted theoretically for model structures. The discrepancies in G₀ could be due to a substitution of an‐ ions and the formation of cation vacancies in η‐Ta₂N₃. Self‐healing behaviour of η‐Ta₂N₃ by mechanical polishing was observed and confirmed by two independent experimental methods. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q

We prove that if $1\le p,q\le \infty$, then the spaces $L_p+L_q$ and $L_p\cap L_q$ are isomorphic if and only if $p=q$. In particular, $L_2+L_{\infty }$ and $L_2\cap L_{\infty }$ are not isomorphic, which is an answer to a question formulated in [2].     

Bulk and surface electron transport in topological insulator candidate YbB6–δ

We report the study of transport and magnetic properties of the YbB_6–δsingle crystals grown by inductive zone melting. A strong disparity in the low temperature resistivity, Seebeck and Hall coefficients is established for the samples with the different level of boron deficiency. The effective parameters of the charge transport in YbB_6–δ are shown to depend on the concentration of intrinsic defects, which is estimated to range from 0.09% to 0.6%. The pronounced variation of Hall mobility μ_H found for bulk holes is induced by the decrease of transport relaxation time from τ ≈ 7.7 fs for YbB_5.994 to τ ≈ 2.2 fs for YbB_5.96. An extra contribution to conductivity from electrons with μ_H≈ –1000 cm² V^–1 s^–1 and the very low concentration n /n_Yb≈ 10^–6 discovered below 20 K for all the single crystals under investigation is suggested to arise from the surface electron states appeared in the inversion layer due to the band bending. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.     

Functional a posteriori error estimates for incremental models in elasto-plasticity

We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.      

Feature of the magnetotransport of a quasi-one-dimensional electrons on the superfluid helium

The magnetotransport in a nondegenerate quasi-one-dimensional (Q1D) electron system over superfluid helium has been investigated experimentally. The measurements are performed in the presence of a perpendicular magnetic field B up to 2.6 T in the temperature range T=0.48–2.05 K in the system of conducting channels of 100–400 nm width. It is shown that the value of longitudinal magnetoresistance ρ_xx increases with B. In the electron-gas scattering region (T>0.9 ), the behaviour of ρ_xx agrees with classical Drude law. In the quantum transport regime, the self-consistent Born approximation (SCBA) theory for a 2D electron system over liquid helium describes the experimental data qualitatively. The deviation due to the difference of the experimentally studied Q1D system of the electrons in a parabolic potential well differs from theoretically analysed one. The experimental data agree with the theoretical calculation for the Q1D electron system at the weak magnetic field and the low temperature.

The negative magnetoresistance of the conducting channels has been observed in both the gas- and the ripplon-scattering region. These effects have been explained by weak carrier localization on the gas atoms at high temperature and by display of the quantum magnetotransport features in a mesoscopic system at low temperature.